This project will develop transcranial magnetic stimulation coils with improved focality and depth (fdTMS). TMS is a technique for noninvasive brain stimulation using strong, brief magnetic pulses. TMS is widely used in the neurosciences as a tool for probing brain function and connectivity. Presently, TMS is FDA-approved for the treatment of depression and for pre-surgical cortical mapping, and is under study for other psychiatric and neurological disorders. A significant limitation of TMS, however, is that the induced electric field stimulates a relatively large area of cortex, especially when the targets are deep. Low focality entails co-activation outside the desired target, which reduces the precision of stimulation, may increase the risk of side-effects including seizures, and may reduce efficacy via antagonistic responses. Thus, fdTMS coil technology could enable more selective, safe, and effective stimulation. Conventional TMS coil design has relied on simple heuristics to determine the shape of the coil windings. Because the winding shape is related in a complex way to the electric field induced in the brain, the spatial stimulation characteristics of available coils are generally suboptimal. Consequently, while coils intended specifically for deep TMS have been commercialized, their tradeoff between depth and focality is not better than that of conventional figure-8 and double-cone configurations. Addressing this limitation, we propose to develop fdTMS coils to obtain maximal focality for a given depth of stimulation or specific anatomical target. Unlike conventional approaches, our method specifies the required electric field characteristics in the brain and deploys novel computational optimization algorithms to determine the coil winding shape and placement to meet these specifications within practical energy limits. We present preliminary data demonstrating that for any target depth our approach outperforms existing coils with increase in focality up to 100%. Using this approach, we will design, implement, and validate two types of fdTMS coils. First, we will develop a series of general-purpose coil designs corresponding to a range of practical depths. The coils will be optimized for maximal focality in a spherical head model, reflecting the intended use for various targets and therefore being anatomy-independent. Like most conventional coils, they will be freely moveable on the head surface. Second, we will optimize coils for specific anatomical brain targets using state-of-the-art MRI-based head models. This approach accounts for the effects on the induced electric field of anatomical features such as gyral shape and current flow through the highly conducting sulci. We will validate experimentally the fdTMS coils via measurements of induced electric field maps as well as human motor responses. The human study will quantify stimulation focality and depth through mapping of muscle representations at various locations and depths in the primary motor cortex using electromyography.